"Potrzebuję jego, a nie ciebie" (I need him, not you) would be a correct sentence, as 'jego' would be accented and show the contrast between 'him' and 'you'. Simple "I need him" will be said exactly as here.

Also this sentence just showed me not to take everything written on wiktionary absolutely-totally-literally. Usually the short forms of pronouns (like mi, ci, go) shouldn't be put at the end of the sentence, but in this very short sentence it's definitely the right form.

Rather 'in a context', I'd say... but generally yes, it would. "Widzisz ten komputer? Potrzebuję go!" = "You see this computer? I need it!"